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Mirrors > Home > NFE Home > Th. List > biimpac | GIF version |
Description: Inference from a logical equivalence. (Contributed by NM, 3-May-1994.) |
Ref | Expression |
---|---|
biimpa.1 | ⊢ (φ → (ψ ↔ χ)) |
Ref | Expression |
---|---|
biimpac | ⊢ ((ψ ∧ φ) → χ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | biimpa.1 | . . 3 ⊢ (φ → (ψ ↔ χ)) | |
2 | 1 | biimpcd 215 | . 2 ⊢ (ψ → (φ → χ)) |
3 | 2 | imp 418 | 1 ⊢ ((ψ ∧ φ) → χ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 176 ∧ wa 358 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 |
This theorem depends on definitions: df-bi 177 df-an 360 |
This theorem is referenced by: gencbvex2 2902 2reu5 3044 vfinspsslem1 4550 phi11lem1 4595 0cnelphi 4597 ideqg2 4869 nfunsn 5353 leltctr 6212 tlecg 6230 nchoicelem3 6291 |
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